What is derivative of y^2x^3+x^2+y=7 ?

The answer to derivative of y^2x^3+x^2+y=7 is (dy)/(dx)=(-3x^2y^2-2x)/(2x^3y+1)

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derivative of y^2x^3+x^2+y=7

derivative of

y^{2} x^{3} + x^{2} + y = 7

\frac{d y}{d x} = \frac{- 3 x ^{2} y ^{2} - 2 x}{2 x ^{3} y + 1}

Solution steps

y^{2} x^{3} + x^{2} + y = 7

Treat

y

y (x)

Differentiate both sides:

2 y \frac{d y}{d x} x^{3} + 3 x^{2} y^{2} + 2 x + \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 3 x ^{2} y ^{2} - 2 x}{2 x ^{3} y + 1}

\frac{d y}{d x} = \frac{- 3 x ^{2} y ^{2} - 2 x}{2 x ^{3} y + 1}

sin^{2} (y) + cos (x) y = k

s = \frac{t ^{2} + 4}{2}

x y = y^{2}

x^{3} y^{2} - 2 y = 4

y + sin (y) = x^{2}

What is derivative of y^2x^3+x^2+y=7 ?
The answer to derivative of y^2x^3+x^2+y=7 is (dy)/(dx)=(-3x^2y^2-2x)/(2x^3y+1)